Service demands and visit ratios of an isolated subnetwork, from the stochastic complement of its routing matrix. More...

#include <cmath>
#include <cstddef>
#include <vector>
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/linalg.h"
#include "line/util/lu.h"
#include "line/util/matrix.h"

Include dependency graph for fes_build_isolated.h:

Classes
struct	line::fes::FesIsolated< T >
	Demands and visit ratios of the isolated subnetwork. More...

Namespaces
namespace	line
namespace	line::fes

Functions
template<class T>
FesIsolated< T >	line::fes::fes_build_isolated (const Matrix< T > &rates, const Matrix< T > &stochCompS)
	Build the isolated subnetwork's demands and visit ratios.

Detailed Description

Service demands and visit ratios of an isolated subnetwork, from the stochastic complement of its routing matrix.

Templated port of matlab/src/api/fes/fes_build_isolated.m. Given the stochastic complement S of the routing chain restricted to a subset of stations, the per-class visit ratios are the stationary distribution of the embedded DTMC of that class,

v_k P_k = v_k,   sum_i v_k(i) = 1,

and the demands follow as L(i,k) = v_k(i) / rate(i,k), renormalized so that the first station of the subset is visited once, which is the MVA convention the flow-equivalent-server construction expects.

THE sn DEPENDENCY IS LIFTED INTO THE SIGNATURE. The MATLAB entry point takes (sn, subsetIndices, stochCompS) and opens with a loop that plucks five fields out of sn – nclasses, stationToNode, nodetype, nservers, rates – to produce the per-station server counts, the delay flags and the service rates of the subset. Nothing after that loop reads sn, and the routing already arrives as a plain matrix argument. The extraction is therefore not part of the algorithm: this port takes the extracted quantities directly, in the same spirit as npfqn_sqd.

Note in particular that mi and isDelay are PURE PASS-THROUGH in the reference: they are assembled from sn and returned, and no later line reads them. They are not arguments here for that reason – a caller that wants them holds them already. The numeric core needs only the service rates and the stochastic complement.

INDEXING. stochCompS is indexed (station-1)*K + class over the SUBSET, so it is (M_sub K x M_sub K); the reference forms it that way and indexes it with the subset position i, not the original station id. Its class-k block is read at rows and columns (i-1)*K + k.

ARITHMETIC. Exact at Rational. The stationary distribution is obtained from the singular system (I - P_k' + e e'/M) x = e/M, one linear solve per class, which is a finite sequence of field operations; there is no iteration and no tolerance in the solve itself. The two guards that DO carry a tolerance are reproduced from the reference and are structural rather than numerical: a row of P_k whose sum is below FineTol = 1e-8 is treated as "no routing defined" and made a self-loop, and a row whose sum differs from one by more than FineTol is renormalized. At Rational a caller supplying an exactly stochastic complement never reaches either branch.

DIVERGENCE, stated because it changes which inputs take the fallback path. The reference guards the solve with rank(A) == M_sub and substitutes the uniform distribution when the rank is deficient. A rank test is a singular value decomposition, which is double-only in this tree and has no exact instantiation (util/eig.h documents why). The port instead attempts the solve and takes the same uniform fallback when the factorization finds an exactly zero pivot. The two agree on every non-degenerate input: A is nonsingular precisely when the class-k chain has a unique stationary distribution, which is when the solve succeeds. They can differ only for a matrix that is numerically rank deficient yet still factorizable, where the reference falls back and the port returns the (ill-conditioned) solve; that is the direction that preserves information rather than discarding it.

Definition in file fes_build_isolated.h.

Classes

Namespaces

Functions

Detailed Description